News of the blunder was a "kick in the gut" to an already underfunded CDHB, Keown said.

"Staff are working their butts off to deliver services for the community and meet the ministry's targets despite continuous under funding".

He said nearly all DHBs ran a deficit, which was a sign they were not getting enough money rather than a sign of poor management, as the ministry had implied.

"It's a bit rich for the ministry to tell DHBs how to balance their books when they can't manage theirs."

Kane said Chuah should be made accountable for his mistakes.

The CDHB had a difficult working relationship with Chuah, whom she believed was a "huge block" in its relationship with the ministry.

"I don't have any confidence in the ministry. They can't even understand their own data."

The CDHB had been underfunded for years because ministry population data did not take into account a shift in deprivation, an increase in the number of migrant workers and an ageing population, she said.

Board member Andy Dickerson would not comment on whether Chuah should resign.

He said the mistake compounded the "continued under funding of Canterbury health services at a time when we are still recovering from the worst natural disaster in New Zealand's history".

CDHB board member Anna Crighton would not comment on Chuah, but said the "continual misinformation the ministry is using to allocate our funding is extremely concerning".

"It's been going on for several years. It's a continual fight to get a fair health dollar that equates to the same level as other comparable health boards.

"It's extraordinary behaviour from a ministry who is supposed to be supporting us."

Consultancy firm Deloitte was called in to conduct an independent review of the ministry's procedures.​

CDHB acting chief executive Mary Gordon said the organisation was revisiting its draft annual plan around funding allocation, which was "a considerable piece of work".

JOSEPH JOHNSON/FAIRFAX NZ

CDHB board member Aaron Keown says Chai Chuah should resign.

"At this stage the financial loss and its impacts on particular services are still unknown."

Chuah said he had apologised for the mistake last week and his focus was working with the independent review "to ensure it doesn't happen again".

"It has been a very disappointing incident and I must take responsibility for it."

He rejected claims the CDHB was under funded.

"Canterbury DHB's current budget is $1.4 billion, up $331 million on eight years ago."

The Government provided an additional $106 million in funding since 2011 to help the DHB respond to earthquake related pressures, he said.

The formula used to determine what funding each DHB received was based on official census and population data from Statistics New Zealand.

"The formula also takes into account the number of people who live in each DHB catchment, their age, socio-economic status, ethnicity, and sex. It also has mechanisms to compensate DHBs who service rural communities and areas of high deprivation."